A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Compass Construction of Bézier Curves and B-Splines
https://orcid.org/http://orcid.org/0000-0002-8125-1850
This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are presented which are used to locate points on any Bézier curve or B-Spline by using an abstract compass. These constructions aim to translate the B-Spline definition of Paul de Casteljau into the modified versions of compass-only constructions explained by Aleksandr Kostovskii. Several computer scripts are developed and used to simulate these constructions while calculating and minimizing their computational complexities. The mathematical bridge explained in this article is expected to bring back to mind the synthetic and axiomatic roots of design geometries.
Compass Construction of Bézier Curves and B-Splines
https://orcid.org/http://orcid.org/0000-0002-8125-1850
This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are presented which are used to locate points on any Bézier curve or B-Spline by using an abstract compass. These constructions aim to translate the B-Spline definition of Paul de Casteljau into the modified versions of compass-only constructions explained by Aleksandr Kostovskii. Several computer scripts are developed and used to simulate these constructions while calculating and minimizing their computational complexities. The mathematical bridge explained in this article is expected to bring back to mind the synthetic and axiomatic roots of design geometries.
Compass Construction of Bézier Curves and B-Splines
https://orcid.org/http://orcid.org/0000-0002-8125-1850
This article reveals a mathematical bridge between compass-only geometric constructions and parametric curves. A set of construction algorithms are presented which are used to locate points on any Bézier curve or B-Spline by using an abstract compass. These constructions aim to translate the B-Spline definition of Paul de Casteljau into the modified versions of compass-only constructions explained by Aleksandr Kostovskii. Several computer scripts are developed and used to simulate these constructions while calculating and minimizing their computational complexities. The mathematical bridge explained in this article is expected to bring back to mind the synthetic and axiomatic roots of design geometries.
Compass Construction of Bézier Curves and B-Splines
Nexus Netw J
Yazar, Tuğrul (author)
Nexus Network Journal ; 23 ; 789-811
2021-09-01
23 pages
Article (Journal)
Electronic Resource
English
Compass Construction of Bézier Curves and B-Splines
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